WEBVTT 00:00:01.960 --> 00:00:06.099 In the 18th century, the city of Konigsberg was 00:00:06.099 --> 00:00:09.619 divided by a river. Seven bridges connected its 00:00:09.619 --> 00:00:13.080 two banks and two islands. Residents wondered 00:00:13.080 --> 00:00:16.280 whether it was possible to take a walk that crossed 00:00:16.280 --> 00:00:21.019 every bridge exactly once. People tried many 00:00:21.019 --> 00:00:23.539 routes. They could begin at different places 00:00:23.539 --> 00:00:25.780 and they could cross the bridge in different 00:00:25.780 --> 00:00:31.039 order. But every attempt failed. Then enter Leonard 00:00:31.039 --> 00:00:34.219 Euler. Euler approached the problem differently. 00:00:34.600 --> 00:00:38.539 He realized that the precise distances and directions 00:00:38.539 --> 00:00:43.579 and shape of the bridges did not matter. He replaced 00:00:43.579 --> 00:00:47.859 every region of land with a point and each bridge 00:00:47.859 --> 00:00:52.920 with a line. The complicated map became a simple 00:00:52.920 --> 00:00:56.939 network. Then Euler counted how many lines met 00:00:56.939 --> 00:01:00.280 at each point. Every time a traveler enters a 00:01:00.280 --> 00:01:04.379 point, another bridge is needed. So most points 00:01:04.379 --> 00:01:07.920 in a successful route must have an even number 00:01:07.920 --> 00:01:12.120 of bridges. Konigsberg had four points with an 00:01:12.120 --> 00:01:16.859 odd number. So the desired walk was not possible. 00:01:17.879 --> 00:01:21.140 Euler solved the problem by changing its representation. 00:01:21.760 --> 00:01:25.599 He let go of the details that seemed essential. 00:01:26.459 --> 00:01:28.780 and discovered a structure that had previously 00:01:28.780 --> 00:01:32.859 been hidden. His insight helped begin what we 00:01:32.859 --> 00:01:36.359 now call graph theory. It's a branch of math 00:01:36.359 --> 00:01:39.659 that's used to study transportation, communication, 00:01:40.239 --> 00:01:46.079 social networks, and a lot more. Now, Euler also 00:01:46.079 --> 00:01:48.459 faced a profound change in his personal life. 00:01:49.040 --> 00:01:53.159 His eyesight deteriorated over many years, and 00:01:53.159 --> 00:01:56.760 he eventually would become nearly blind. And 00:01:56.760 --> 00:02:01.519 yet, he continued to produce math at an extraordinary 00:02:01.519 --> 00:02:05.180 rate. Now, it may be tempting to tell that this 00:02:05.180 --> 00:02:09.860 is a simple story of heroic determination. Euler 00:02:09.860 --> 00:02:13.439 overcame blindness because his mind was powerful 00:02:13.439 --> 00:02:17.340 enough. But I think the fuller story is better. 00:02:17.599 --> 00:02:22.280 Because Euler adapted. But he did not work alone. 00:02:22.919 --> 00:02:27.159 He relied on his exceptional memory, yes, dictated 00:02:27.159 --> 00:02:31.000 calculations, and received substantial help from 00:02:31.000 --> 00:02:33.960 his sons and others, including colleagues and 00:02:33.960 --> 00:02:39.259 assistants. His continued work was possible by 00:02:39.259 --> 00:02:43.319 both personal perseverance and a community willing 00:02:43.319 --> 00:02:46.240 to change how mathematics work would be done. 00:02:47.210 --> 00:02:50.509 Now, Euler's blindness was not a gift, and we 00:02:50.509 --> 00:02:52.750 do not need to pretend that losing his sight 00:02:52.750 --> 00:02:56.310 made him a better mathematician. But Euler found 00:02:56.310 --> 00:03:00.389 meaning not by declaring the loss good, but in 00:03:00.389 --> 00:03:05.169 his response. He changed his methods. He accepted 00:03:05.169 --> 00:03:08.710 help. And he continued to participate in the 00:03:08.710 --> 00:03:12.789 work he valued. When I encounter a limitation, 00:03:13.069 --> 00:03:16.330 sometimes I keep trying the same route with greater 00:03:16.330 --> 00:03:20.530 force. Euler's mathematics suggests another possibility. 00:03:21.189 --> 00:03:24.050 Perhaps the problem can be represented differently. 00:03:24.810 --> 00:03:28.409 Or perhaps a tool or maybe a collaborator or 00:03:28.409 --> 00:03:31.349 another method can make another route possible. 00:03:32.610 --> 00:03:36.110 What limitation are you currently treating as 00:03:36.110 --> 00:03:41.229 a command to stop? Could it instead be an invitation 00:03:41.229 --> 00:03:45.449 to change the map? Or maybe just to ask for help? 00:03:45.750 --> 00:03:48.110 Or maybe find another way across?